Simplify the following expression: $a = \dfrac{-36z + 18}{-54z + 6}$ You can assume $z \neq 0$.
Find the greatest common factor of the numerator and denominator. The numerator can be factored: $-36z + 18 = - (2\cdot2\cdot3\cdot3 \cdot z) + (2\cdot3\cdot3)$ The denominator can be factored: $-54z + 6 = - (2\cdot3\cdot3\cdot3 \cdot z) + (2\cdot3)$ The greatest common factor of all the terms is $6$ Factoring out $6$ gives us: $a = \dfrac{(6)(-6z + 3)}{(6)(-9z + 1)}$ Dividing both the numerator and denominator by $6$ gives: $a = \dfrac{-6z + 3}{-9z + 1}$